"Is this safe to shoot in my revolver?"

Yes. The .32 WCF (.32-20) was designed as a rifle cartidge for the Winchester 1873. Around 1882, Colt chambered it in their Single Action Army. That's why it is listed as a rifle cartridge.

The only factory load to avoid is the 80 grain jacketed hollowpoint that has a "HV" (high velocity) headstamp. IIRC, that load hasn't been produced since the 1960s.

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John 3:16
WAR EAGLE!